Geodesic
Solution of the eigenvalue problem for a regular pencil $\lambda A_0-A_1$ with singular matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 70 (1977), pp. 103-123 
V. N. Kublanovskaya; T. Ya. Kon'kova. Solution of the eigenvalue problem for a regular pencil $\lambda A_0-A_1$ with singular matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms, Tome 70 (1977), pp. 103-123. http://geodesic.mathdoc.fr/item/ZNSL_1977_70_a6/
@article{ZNSL_1977_70_a6,
     author = {V. N. Kublanovskaya and T. Ya. Kon'kova},
     title = {Solution of the eigenvalue problem for a regular pencil $\lambda A_0-A_1$ with singular matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {103--123},
     year = {1977},
     volume = {70},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_70_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

One considers the generalized eigenvalue problem \begin{equation} (A_0\lambda-A_1)x=0, \end{equation} when one or both matrices $A_0$, $A_1$ are singular and ker $\operatorname{ker}A_0\cap\operatorname{ker}A_1=\varnothing$ is the empty set. With the aid of the normalized process, the solving of problem (1) reduces to the solving of the eigenvalue problem of a constant matrix of order $r=\min(r_0,r_1)$, where $r_0$, $r_1$ are the ranks of the matrices $A_0$, $A_1$, which are determined at the normalized decomposition of the matrices. One gives an Algol program which performs the presented algorithm and testing examples.